Tag Archives: interference

Nonlinear effects in shallow water waves

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I recently googled for something related to the shape of waves and came across a photo of a wave that caught my eye, and it took me to a journey that lead to the article “nonlinear shallow ocean wave soliton interactions on flat beaches” by Ablowitz and Baldwin (2012).

What’s discussed in that article is that while many wave interactions can be seen as (more or less) linear, sometimes there are nonlinear effects that can be replicated in a model. So far so not surprising. But I got fascinated because the phenomenon they look at I have seen over and over again and never really paid any attention to it: Wave crests forming X or Y shapes. But looking through my archives, I even had dozens of pictures of this exact phenomenon! (Actually, I didn’t have to look further back than to a beautiful day last November, when I also observed the wavelength dependency of wave-object interactions)

Take for example the picture below: Do you see the H shape in the waves closest to shore? (In the article they would probably call it a more-complex shape, since it’s a double Y shape…)

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Below I’ve drawn into the picture what I mean by H-shape in green, and the typical kind of linear wave interaction in red (all crests just move on without influencing each other except in the spot where they occur at the same time, there they just add to each other):

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Or below, I spot an X-shape:

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And here are several X- and Y-shapes

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And the picture below just to give you an orientation of where you are: Yep, it’s the same spot where we usually observe foam stripes, funny waves, or ice…

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Mark J. Ablowitz, & Douglas E. Baldwin (2012). Nonlinear shallow ocean wave soliton interactions on flat beaches Physical Review E, vol. 86(3), pp. 036305 (2012) arXiv: 1208.2904v1

Interference of one wave field with its reflection and a second wave field

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All you regular readers of my book and my blog surely recognize what’s going on below?

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Yes! A wave field comes in at an angle to the pier and gets reflected, leading to a chequered pattern. And a second wave field comes in with wave crests pretty much parallel to the pier, adding a little more interest to the pattern.

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I love watching these kinds of waves! But it is really difficult to take good pictures. Sorry about the over-exposed background…

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But it is so beautiful!

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Wave-watching

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Do you know the feeling when you, even on the most beautiful of days, want to get out of the pretty parks as quickly as possible so you can finally see the water?

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Especially when it’s foggy?

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And it is so worth it, there is always something to see. For example on that day: what a nice field of shallow water waves!

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And what an awesome criss-crossing of waves being reflected on the sea wall on which I was standing when taking that picture.

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And how sad that this lake was frozen over! :-)

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P.S.: Still looking for a christmas present for your nerdy friend, your niece, anyone who should spend more time looking at water? Check out my book :-)

Wavelength dependency of wave-object-interactions

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Wavelength dependency of wave-object-interactions. What a title! :-) But that is exactly what I observed over the enormous timespan of three full minutes (as shown by the time stamps of my camera) when I went strolling along Kiel Fjord one Saturday morning.

First, I saw this old, overgrown tyre in a wave field that was dominated by small wind waves. We clearly see how they are diffracted around the tyre and how there is a nice interference pattern downwind of the tyre (to the left in the picture below).

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Tyre in the Kiel Fjord and diffraction of small wind waves around it, leading to a beautiful interference pattern to the left of the tyre

Also I quite like how there are absolutely no waves inside the tire, where the wind is shaded off by the tyre and the stuff growing on it.

Then, a really short while later, the wave field was dominated by longer waves running in from the distance. Below, we still see remnants of the old interference pattern to the left of the tyre, but also how the longer waves run around it. In the picture below, the wave crest that was broken up by the tyre is about to rejoin.

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And then, only an instant later, this is what the wave field looked like. Hardly and ripples caused by local wind, but many short waves. No real interaction between tyre and waves visible any more.

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Isn’t that fascinating? And it all happened within three minutes! :-)

P.S.: Still looking for a christmas present for your nephew, your friends’ kid, your geeky friend? Check out my book! :-)

If waves spread equally in all directions, then how come we see linear wakes?

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If waves spread equally in each direction along the water’s surface, then how come ships (or ducks) have wakes that are just those long lines of waves and not circular at all?
So. Kids are typically familiar with what it looks like when you throw stuff in the water (for proof see below: my godchild on a “Tour de Ruhr” where I learned tons of stuff about mining in Germany. I had no idea that stuff was so interesting! Anyway, I digress. Obviously you had to throw stuff in the water when the reflections are this awesome!)
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But then wakes are seemingly behaving in a very different way. For a nice example of a wake, see the movie below. In that movie, you are looking backward from a boat at its starboard wake. The boat has been sailing straight ahead for a bit after turning to the starboard side (and you will see the resulting curve in the wave in the movie).
Even though slightly curved due to the ship’s change in heading, that wave clearly doesn’t look like a ring around the boat (from where I found the video on my phone I think it must have been a touristy boat in Bergen that I went on with my friend Leela).
So. Good question, isn’t it? Why does the wave look straight? Now don’t tell me it has something to do with interference and stuff, because I need to explain it to a young kid.
I have attempted an explanation, but I am really not sure if it works. What do you think? Check it out and let me know!
The image below shows a sketch of what it looks like if you throw a pebble into the water (or the pattern a raindrop would make). Ideally, we would only see one ring, but since a secondary drop is typically thrown into the air (and sometimes a tertiary) let’s work with three concentrical rings of waves so that the pattern looks as much as possible like what the kid would be likely to observe. The fading colors indicate that the second and third ring have a smaller amplitude than the first one (whose amplitude should be decreasing as time goes on, but let’s not get too technical here…).
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So now how to go from the pebble to the wake? Continuous pebble drops!
From this we have the bow wave and the choppy water inside those two rays of waves. Of course, there we would also have turbulence due to the ship’s propeller or the duck’s feet etc, but maybe this is enough for now?
Except to add that those kind of waves are shock waves (the source of the waves traveling faster than wave speed) — in 3D and in air, the same physics would lead to sonic boom! :-)
Waves on Aasee in Münster. By Mirjam S. Glessmer

Wave hunt expedition. You don’t need to live close to the coast to observe all kinds of wave phenomena!

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A 1.5 hour walk around a lake — and 242 photos of said lake — later I can tell you one thing: You definitely don’t need to live close to the coast in order to observe wave phenomena!

The idea to go on a “wave hunt expedition” is actually not mine (although it definitely sounds like something I could have come up with!), it’s Robinson’s idea. Robinson had students go on wave hunt expeditions as part of their examination, and present their results in a poster. I was so impressed with that, that I had to do it myself. Obviously. So the second best thing about work travel (right after the best thing, again, obviously!) is that I find myself in a strange place with time on my hand to wander around and explore. Not that Münster might not have been a nice city to explore, but the lake…

Anyway. I only want to show you 53 out of the 242 pictures. I was going to annotate all of them so you actually see what I mean. And I started annotating. But since I am giving a workshop tomorrow (which is all prepared and ready, but I do need my beauty sleep!) I only drew the key features in the pictures, and you will have to come up with the correct keywords all by yourself (have your pick: refraction! diffraction! fetch! interference! :-)) So click through the gallery below and see first the original photo and then one that I drew in. Do you spot the same stuff that I saw, or what else do you see? Let me know!

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If you think it would be useful to see all those pictures with proper annotations and descriptions at some point please let me know. I might still be excited enough to actually do it, who knows…

P.S.: I actually really enjoy work travel for the work parts, too. For example, I went to a great workshop in Dortmund earlier this year to learn about a quality framework for quantitative research, and that workshop was amazing. And a week ago, I went to Stuttgart for a meeting with all the fellows of the Stifterverband für die Deutsche Wissenschaft, which was also great. And now I am giving this workshop in Münster, that I am actually really excited about because I managed to condense pretty much all I know about “active learning in large groups” into a 2.5 hour workshop. Just so you don’t get the wrong idea about my priorities. Obviously water comes first, but then work is a very close second ;-)

Wave phenomena on the Pinnau in Mölln. By Mirjam S. Glessmer

Observing hydrodynamic phenomena on a creek

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Looking at a creek on a Sunday stroll, and seeing lots and lots of concepts from hydrodynamics class.

For example below, you see waves radiating from each of the ducks. And you see interference of waves from all those ducks.

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What happens if the ducks bring their waves closer?

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At some point, all those waves from the ducks are going to hit the weir in the picture below.

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And there, they are going to somehow react to the flow field caused by the changes in topography.

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And you can spot so many different phenomena: Standing waves, hydraulic jumps, and lots more!

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Watch the movie below to see the whole thing even better!

Btw, you might remember this spot, I have talked about standing waves from right there before. Interestingly, the wave pattern in the other post looks really different, probably due to different water levels or changes in topography (maybe someone threw in rocks or they did some construction work on the weir?). But it is still just as fascinating as last time :-)

And for those of you who like to see a “making of”:

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More interference of waves, this time as seen “at sea”

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“At sea” in quotes, because technically we were at the mouth of the Weser river… But still! (deutscher Text unten)

The really exciting thing working with the kids here at the JuniorAkademie is that they are really good at transferring things that we talk about theoretically to what they see in a tank experiment, and even to what they see on the “real ocean”.

The day before we went on the student cruise, we did the wave interference experiments described here and here. But then “at sea” they saw a situation similarly to the one I filmed and posted below and they got so excited to see the same phenomena for real. One kid said that before, he couldn’t see the waves for the wave (alluding to not being able to see the wood for the trees), but that it was so cool to look at the water and see so much physics. Those are the moments we teach for, aren’t they? :-)

Das wirklich spannende daran, hier bei der JuniorAkademie zu unterrichten ist, dass die Jugendlichen sehr gut darin sind, das theoretisch erlernte Wissen (wobei wir uns sehr bemühen, nicht über Theorie an die Dinge heran zu gehen!) auf praktische Situationen zu übertragen und die Phänomene wieder zu erkennen – sowohl im Tank als auch “auf See”. “Auf See” in Anführungszeichen, weil die Wesermündung natürlich noch nicht so richtig zur See zählt, aber immerhin.

Am Tag vor der Ausfahrt haben wir die Interferenzexperimente gemacht, die ich hier und hier beschrieben hatte. Aber dann “auf See” waren mehrere Jugendliche wirklich begeistert, als sie eine Situation beobachtet haben die so ähnlich war wie die, die ich gefilmt habe (Siehe Film unten). Ein Teilnehmer sagte, dass er vor unserem Workshop “die Wellen vor Wellen nicht” gesehen habe, in Anlehnung an “den Wald vor Bäumen nicht sehen”. Jetzt aber sei er total begeistert und fasziniert davon, aufs Wasser zu gucken und so viel Physik zu sehen. Das ist ja eigentlich das beste Kompliment, das wir als Lehrer bekommen können.

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Wave interference in a tank

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Creating waves and watching them interfere. (deutscher Text unten)

You might not have guessed it from reading about our waves meeting over a sandbank experiment, but we weren’t doing in purely for its entertainment value. Our goal was to see how waves interfere, because the theory of interfering waves seems to be counter-intuitive in some cases. A second experiment we have been doing on this topic is shown below. We create waves by dripping water drops on the water surface and film (and in some cases also watch) from below. Movie at the end of this post!

Obwohl es sicherlich nicht danach aussah, haben wir das  Experiment mit den Wellen auf der Sandbank nicht nur aus Spaß veranstaltet, sondern durchaus mit einem wissenschaftlichen Hintergrund: Wir wollten uns ansehen, wie sich mehrere Wellen überlagern.

Von oben werden Wassertropfen in den Tank getropft, das daraus entstehende Wellenfeld wird von unten gefilmt (und in einigen Fällen auch beobachtet).